Topics in ergodic theory
Topics include basic ergodic theorems, recurrence, mixing, conditional measures, factors, joinings, Furstenbergs proof of Roths theorem, nilrotations and their connection to multiple recurrence, actions of locally compact groups, geodesic flow on quotients of hyperbolic plane.
Students are assumed to have some background in measure theory and functional analysis.
A good online source for the material of the course as well as background material is the book Ergodic Theory: with a view towards Number Theory Einsiedler and Ward.
Other sources include:
"Recurrence in ergodic theory and combinatorial number theory" by Furstenberg,
"Ergodic theory" by Peterson,
"Ergodic theory via joinings" by Glasner,
"Combinatorial and Diophantine applications of ergodic theory" Handbook of dynamical systems. Vol. 1B, 745--869, Elsevier B. V., Amsterdam, 2006.
Some other online resources:
Terry Tao's blog
Ben Green's notes
Akshay Venkatesh's lecture
notes